Distribution values predictors
Frequency outcome variable
Distribution of response types across RelX and RelY
Model effect relative position of referents
con_mat <- cbind(c(2, -1, -1), c(0, 1, -1))
contrasts(data$condition) <- con_mat
model1 <- glmer(response1 ~ relY + relX + relY:relX + (1 + relY|id), data = data, family = binomial("logit"), glmerControl(optimizer="bobyqa", optCtrl = list(maxfun = 100000)))
summary(model1)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: response1 ~ relY + relX + relY:relX + (1 + relY | id)
## Data: data
## Control:
## glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+05))
##
## AIC BIC logLik deviance df.resid
## 36040.5 36099.0 -18013.3 36026.5 31387
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -9.8915 -0.7995 0.1095 0.7984 15.3916
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 0.003348 0.05786
## relY 5.539862 2.35369 -0.54
## Number of obs: 31394, groups: id, 80
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.01410 0.01454 0.970 0.332
## relY -2.58403 0.26641 -9.699 <2e-16 ***
## relX 0.31590 0.01886 16.750 <2e-16 ***
## relY:relX 0.04028 0.05925 0.680 0.497
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) relY relX
## relY -0.237
## relX -0.014 -0.010
## relY:relX -0.050 -0.003 0.008
Effect of social context: Model comparison
model2 <- glmer(response1 ~ relY + relX + relY:relX + relY: condition + relX:condition + relY:relX:condition + (1+ relY|id), data = data, family = binomial("logit"), glmerControl(optimizer="bobyqa", optCtrl = list(maxfun = 100000)))
anova(model1, model2)
## Data: data
## Models:
## model1: response1 ~ relY + relX + relY:relX + (1 + relY | id)
## model2: response1 ~ relY + relX + relY:relX + relY:condition + relX:condition +
## model2: relY:relX:condition + (1 + relY | id)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## model1 7 36041 36099 -18013 36027
## model2 13 36036 36144 -18005 36010 16.794 6 0.01007 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Effect of social context: Model summary
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula:
## response1 ~ relY + relX + relY:relX + relY:condition + relX:condition +
## relY:relX:condition + (1 + relY | id)
## Data: data
## Control:
## glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+05))
##
## AIC BIC logLik deviance df.resid
## 36035.7 36144.3 -18004.9 36009.7 31381
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -10.0996 -0.7994 0.1078 0.7968 16.0036
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 0.003288 0.05734
## relY 5.547638 2.35534 -0.54
## Number of obs: 31394, groups: id, 80
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.0142272 0.0145196 0.980 0.3272
## relY -2.5861324 0.2666052 -9.700 <2e-16 ***
## relX 0.3164362 0.0188695 16.770 <2e-16 ***
## relY:relX 0.0385945 0.0592855 0.651 0.5151
## relY:condition1 -0.0686767 0.0272873 -2.517 0.0118 *
## relY:condition2 -0.1145488 0.0467048 -2.453 0.0142 *
## relX:condition1 -0.0010535 0.0133574 -0.079 0.9371
## relX:condition2 0.0499000 0.0230121 2.168 0.0301 *
## relY:relX:condition1 -0.0006996 0.0418850 -0.017 0.9867
## relY:relX:condition2 -0.0227176 0.0718073 -0.316 0.7517
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) relY relX rlY:rX rlY:c1 rlY:c2 rlX:c1 rlX:c2 rY:X:1
## relY -0.235
## relX -0.014 -0.010
## relY:relX -0.050 -0.003 0.007
## relY:cndtn1 0.000 0.003 0.000 0.003
## relY:cndtn2 -0.003 0.003 -0.011 0.003 -0.010
## relX:cndtn1 0.000 0.000 0.008 0.000 -0.051 0.007
## relX:cndtn2 0.000 -0.002 0.013 -0.006 0.007 -0.052 -0.009
## rlY:rlX:cn1 0.001 0.000 0.000 0.014 -0.023 -0.002 0.007 0.005
## rlY:rlX:cn2 -0.009 0.001 -0.007 0.014 -0.002 -0.027 0.005 0.007 -0.010
Diagnostic plots
All coefficients
Plot effects
predProbs = predict(model2, type="response")
relX <- ggplot(data, aes(relX, predProbs)) +
stat_smooth(method="glm", formula=y~splines::ns(x,3),
alpha=0.2, size=0.5) + xlab("Distance between targets on x axis")+ ylab("Predicted probability of proximal demonstrative") + ggtitle("Effect RelX")
int_x <- ggplot(data, aes(relX, predProbs, color=condition)) +
stat_smooth(method="glm", formula=y~splines::ns(x,3),
alpha=0.2, size=0.5, aes(fill=condition), se = F) + xlab("Distance between targets on x axis")+ ylab("Predicted probability of proximal demonstrative") + ggtitle("Interaction RelX by Condition")
relY <- ggplot(data, aes(relY, predProbs)) +
stat_smooth(method="glm", formula=y~splines::ns(x,3),alpha=0.2, size=0.5) + xlab("Distance between targets on y axis")+ ylab("Predicted probability of proximal demonstrative") + ggtitle("Effect RelY")
int_y <- ggplot(data, aes(relY, predProbs, color=condition)) +
stat_smooth(method="glm", formula=y~splines::ns(x,3),
alpha=0.2, size=0.5, aes(fill=condition), se = F) + xlab("Distance between targets on y axis")+ ylab("Predicted probability of proximal demonstrative") + ggtitle("Interaction RelY by Condition")
relX
int_x
relY
int_y
